11.hs

{-
In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid? -}

import Data.List
import Data.Array



main = do
  contents <- readFile "11.txt"
  let
    nums = map (map read) . map words . lines $ contents :: [[Int]]
    matrix = array ((0,0),(19,19))
                   [((a,b),nums!! a !! b) | a <- [0..19], b <- [0..19]]
    horizIndices =
      [((a,b),(a,b+1),(a,b+2),(a,b+3)) | a <- [0..19], b<- [0..16]]
    vertIndices =
      [((a,b),(a+1,b),(a+2,b),(a+3,b)) | a <- [0..16], b<- [0..19]]
    rightDownDiagIndices =
      [((a,b),(a+1,b+1),(a+2,b+2),(a+3,b+3)) | a <- [0..16], b <- [0..16]]
    leftDownDiagIndices =
      [((a,b),(a+1,b-1),(a+2,b-2),(a+3,b-3)) | a <- [0..16], b <- [3..19]]
    getProduct (a,b,c,d) =
      matrix ! a * matrix ! b * matrix ! c * matrix ! d
    indices = horizIndices ++ vertIndices ++
              rightDownDiagIndices ++ leftDownDiagIndices
  print $ maximum (map getProduct indices)